An example concerning set addition in F_2^n
arXiv: Combinatorics(2017)
摘要
We construct sets $A, B$ a vector space over $mathbb{F}_2$ with the property that $A$ is statistically almost closed under addition by $B$ the sense that $a + b$ almost always lies $A$ when $a in A, b in B$, but which is extremely far from being combinatorially almost closed under addition by $B$: if $Au0027 subset A$, $Bu0027 subset B$ and $Au0027 + Bu0027$ is comparable size to $Au0027$ then $|Bu0027| lessapprox |B|^{1/2}$.
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